Effect of Strain Rate and Temperature on Tensile and Fracture Performance of AA2050-T84 Alloy

AA2050-T84 alloy is widely used in primary structures of modern transport aircraft. AA2050-T84 is established as a low-density aluminum alloy with improved Young’s modulus, less anisotropy, and temperature-dependent mechanical properties. During flights, loading rate and temperature variation in aircraft engine subsequent parts are commonly observed. The present work focuses on the effect of loading rate and temperature on tensile and fracture properties of the 50 mm thick (2-inch) AA2050-T84 alloy plate. Quasi-static strain rates of 0.01, 0.1, and 1 s−1 at −20 °C, 24 °C and 200 °C are considered. Tensile test results revealed the sensitivity of mechanical properties towards strain rate variations for considered temperatures. The key tensile properties, yield, and ultimate tensile stresses were positive strain rate dependent. However, Young’s modulus and elongation showed negative strain rate dependency. Experimental fracture toughness tests exhibited the lower Plane Strain Fracture Toughness (KIC) at −20 °C compared to 24 °C. Elastic numerical fracture analysis revealed that the crack driving and constraint parameters are positive strain rate dependent and maximum at −20 °C, if plotted and analyzed over the stress ratio. The current results concerning strain rates and temperatures will help in understanding the performance-related issues of AA2050-T84 alloy reported in aircraft applications.


Introduction
Modern aircraft predominantly use lightweight structures to improve the performanceto-weight ratio. The low-density Aluminum alloy is popular among aircraft structures owing to its durable mechanical properties and ease of manufacturability [1,2]. Composites pose tough competition to Aluminum alloys due to their tailor-made properties suited for specific applications. The unpredictable behavior of composites for change in temperature and time, restricted its usage to secondary and tertiary aircraft structures [3]. Currently, the modern transport aircraft primary structures are built by Al-Li alloys. The Lithium addition to aluminum with improved manufacturing methods resulted in the enhancement of specific strength and stiffness of the alloy [4]. However, the higher cost of Al-Li alloy restricted its usage to only aerospace industries.
The apprehensions related to diversifying mechanical properties of 1st and 2nd generation Al-Li alloys directed the complete withdrawal from aerospace applications [2]. Some noteworthy limitations were anisotropic behavior, cracking during manufacturing, and thermal instability-driven lower fracture toughness [2]. The skillful and sophisticated fabrication methods steered the evolution of 3rd generation Al-Li alloys. The spars and ribs of modern transport aircraft are fabricated by a 3rd generation Al-Li alloy, AA2050-T84 [1].

Tensile and Fracture Toughness Test
ASTM E8/E8M-21, the standard test method for tension testing of metallic materials [30], was used for the tensile specimen preparation and testing of AA2050-T84 alloy. Round specimens were extracted in the rolling (along the length of the plate) direction of the AA2050-T84 plate. Figure 1 shows the tensile test specimen dimensions (in mm) used in this study. The main dimensions of the specimen are, gauge diameter (D 0 = 6 mm), gauge length (L 0 = 30 mm), and overall specimen length (L = 65 mm). The tensile specimens were designed, keeping the L 0 /D 0 ratio to 5. In the present work, AA2050-T84 alloy tensile behavior at different strain rates and temperatures are experimentally studied. Experimental fracture toughness tests are conducted using Compact Tension (C(T)) specimens at various temperatures. Furthermore, the effect of strain rate on fracture characterizing parameters in LEFM such as Stress Intensity Factor (KI), T11, and T33 are analyzed numerically for different temperatures. Finally, the AA2050-T84 alloy tensile and fracture behavior dependency on strain rates and temperatures are compared and evaluated for compatibility for aircraft wing structures.

AA2050-T84 Alloy
This study uses a 50 mm thick (2-inch) AA2050-T84 alloy plate to extract the test specimens. The chemical composition of AA2050-T84 alloy in wt% as obtained from the supplier is shown in Table 1. Copper is used in AA2050-T84 to provide high strength, suited for aircraft applications [29]. The Lithium addition is (<1%) restricted to balance between density reduction and increase in Young's modulus of the alloy [3,29].

Tensile and Fracture Toughness Test
ASTM E8 / E8M-21, the standard test method for tension testing of metallic materials [30], was used for the tensile specimen preparation and testing of AA2050-T84 alloy. Round specimens were extracted in the rolling (along the length of the plate) direction of the AA2050-T84 plate. Figure 1 shows the tensile test specimen dimensions (in mm) used in this study. The main dimensions of the specimen are, gauge diameter (D0 = 6 mm), gauge length (L0 = 30 mm), and overall specimen length (L = 65 mm). The tensile specimens were designed, keeping the Lo/D0 ratio to 5. ASTM E399-20a, the standard test method for linear-elastic plane strain fracture toughness of metallic materials [27], was used. The commonly used fracture test specimen for primary aircraft structures is the compact tension (C(T)) specimen shown in Figure 2. The standard dimensions (in mm) are specimen width (W = 25.4 mm), specimen height (H = 2W), and specimen thickness (B) = crack length (a) = 0.5W. The C(T) specimen is extracted, ensuring the crack length in the rolling direction and load application in the transverse directions of the plate. ASTM E399-20a, the standard test method for linear-elastic plane strain fracture toughness of metallic materials [27], was used. The commonly used fracture test specimen for primary aircraft structures is the compact tension (C(T)) specimen shown in Figure 2. The standard dimensions (in mm) are specimen width (W = 25.4 mm), specimen height (H = 2W), and specimen thickness (B) = crack length (a) = 0.5W. The C(T) specimen is extracted, ensuring the crack length in the rolling direction and load application in the transverse directions of the plate.
Flight durations and operations cause the temperature variations of the wing parts. Furthermore, the effect of these variations depends on alloy type and its ductile to brittle transition temperature [31]. However, temperature variations will be high near the aircraft engine (wing components), and the experienced load rates are dynamic. In the present study, the quasi-static strain rates considered in the tensile tests were 0.01, 0.1, and 1 s −1 . The temperatures considered were −20 • C (Sub-zero temperature), 24 • C (Room temperature), and 200 • C (High temperature) [32]. In the tensile and fracture toughness tests, the low-temperature chamber with liquid nitrogen and a high-temperature furnace with forced convection heating was used to maintain the sub-zero and high temperatures. The Servo Electric Universal Testing Machine (UTM) (BISS, Bangalore, India) with 50 kN capacity was used for tensile and fracture toughness tests. In tensile testing, the applied load and deformations were recorded continuously through the load cell and extensometer, respectively. However, along with these, Crack Opening Displacement (COD) gauge (BISS, Bangalore, India) was used to record the relative displacement of two knife edges of the C(T) specimen in the fracture toughness test. These data were further processed to extract the tensile properties and fracture toughness of the AA2050-T84 alloy as per standards [27,30]. Flight durations and operations cause the temperature variations of the wing parts. Furthermore, the effect of these variations depends on alloy type and its ductile to brittle transition temperature [31]. However, temperature variations will be high near the aircraft engine (wing components), and the experienced load rates are dynamic. In the present study, the quasi-static strain rates considered in the tensile tests were 0.01, 0.1, and 1 s −1 . The temperatures considered were −20 °C (Sub-zero temperature), 24 °C (Room temperature), and 200 °C (High temperature) [32]. In the tensile and fracture toughness tests, the low-temperature chamber with liquid nitrogen and a high-temperature furnace with forced convection heating was used to maintain the sub-zero and high temperatures. The Servo Electric Universal Testing Machine (UTM) (BISS, Bangalore, India) with 50 kN capacity was used for tensile and fracture toughness tests. In tensile testing, the applied load and deformations were recorded continuously through the load cell and extensometer, respectively. However, along with these, Crack Opening Displacement (COD) gauge (BISS, Bangalore, India) was used to record the relative displacement of two knife edges of the C(T) specimen in the fracture toughness test. These data were further processed to extract the tensile properties and fracture toughness of the AA2050-T84 alloy as per standards [27,30].

Finite Element Analysis
The crack driving forces and constraints of the C(T) specimen were investigated at different load rates and temperatures using 3D linear elastic finite element analysis (FEA). Half-symmetry is modeled and analyzed using Abaqus (6.14, 2014, Dassault Systemes Simulia Corp., Providence, RI, USA). The Poisson's ratio (ʋ) and Young's modulus (E) obtained from experimentally conducted tensile results at different strain rates and temperatures are used for linear elastic fracture analysis. The output parameters viz. stress intensity factor (KI) and constraint parameter (T11) were extracted using the counter-integral method mentioned in Abaqus post-processor [33]. T33 is calculated by using Equation (1). In Equation (1), ε33 is a strain in the z-direction (thickness direction) extracted along the crack front. The material property input and the KI extraction details were adopted as similar to the work of [22,33].
Half symmetry C(T) meshed model with supports and loading is shown in Figure 3. 20-noded hexahedral elements with reduced integration were used for the meshing. A

Finite Element Analysis
The crack driving forces and constraints of the C(T) specimen were investigated at different load rates and temperatures using 3D linear elastic finite element analysis (FEA). Half-symmetry is modeled and analyzed using Abaqus (6.14, 2014, Dassault Systemes Simulia Corp., Providence, RI, USA). The Poisson's ratio (v) and Young's modulus (E) obtained from experimentally conducted tensile results at different strain rates and temperatures are used for linear elastic fracture analysis. The output parameters viz. stress intensity factor (K I ) and constraint parameter (T 11 ) were extracted using the counter-integral method mentioned in Abaqus post-processor [33]. T 33 is calculated by using Equation (1). In Equation (1), ε 33 is a strain in the z-direction (thickness direction) extracted along the crack front. The material property input and the K I extraction details were adopted as similar to the work of [22,33].
Half symmetry C(T) meshed model with supports and loading is shown in Figure 3. 20-noded hexahedral elements with reduced integration were used for the meshing. A fine mesh near the crack front was used to encapsulate the crack characteristics effectively. Singularity at the crack front was emulated by shifting the mid-side nodes of crack surrounding elements towards the crack front. The crack edge (crack front) surrounded by these nodes is defined as contour integral. The output parameters are calculated along the user-defined contour integrals (in the present analysis, it is 10 contours). The detailed procedure to define the crack front and contour integrals to obtain crack driving parameters is available in the Abaqus manual [33]. Y-symmetry was imposed along the ligament (the uncracked portion in the crack plane), and the tensile load was applied through the hole to simulate Mode-I. these nodes is defined as contour integral. The output parameters are calculated along the user-defined contour integrals (in the present analysis, it is 10 contours). The detailed procedure to define the crack front and contour integrals to obtain crack driving parameters is available in the Abaqus manual [33]. Y-symmetry was imposed along the ligament (the uncracked portion in the crack plane), and the tensile load was applied through the hole to simulate Mode-I.

Results and Discussions
The following sections discuss the experimental and numerical analysis of the AA2050-T84 alloy.

Tensile Test Analysis
The experimental tensile tests were conducted at varying temperatures and strain rates. A total of 27 tensile tests were conducted, comprising 3 experiments for each strain rate per temperature. The stress-strain curves for different strain rates and temperatures are shown in Figure 4a. The corresponding variation of average tensile properties viz. yield stress (σys), ultimate tensile stress (σut), Young's modulus (E), and % elongation (% et) extracted from the stress-strain curves along with error bars are presented in Figure  4b-e. The positive strain rate dependency was observed for tensile yield stress for the temperatures considered in the study, as shown in Figure 4b. The highest yield stress variation of 2% between 0.01 s −1 to 0.1 s −1 and 0.1 s −1 to 1 s −1 was observed at −20 °C. However, the lowest yield stress variation between successive strain rates, around 0.5%, was noticed at 24 °C. It was observed that the yield stress decreased from −20 °C to room temperature and further increased slightly at 200 °C, indicating the V-shaped behavior for temperature variation.
Similarly, ultimate tensile stress exhibited the positive strain rate dependency at various temperatures, as shown in Figure 4c. However, strain rate has minimal effect on ultimate tensile stress as the difference observed between successive strain rates for all temperatures is less than 1%. The ultimate tensile stress is inversely proportional to the temperature for all the strain rates and is in line with the observations of Hafley et al. [5] and Chemin et al. [6] Figure 4d, shows the variation of Young's modulus at various strain rates and temperatures. Young's modulus showed negative strain rate sensitivity at room and higher temperatures. However, the strain rate effect on Young's modulus was negligible (around

Results and Discussions
The following sections discuss the experimental and numerical analysis of the AA2050-T84 alloy.

Tensile Test Analysis
The experimental tensile tests were conducted at varying temperatures and strain rates. A total of 27 tensile tests were conducted, comprising 3 experiments for each strain rate per temperature. The stress-strain curves for different strain rates and temperatures are shown in Figure 4a. The corresponding variation of average tensile properties viz. yield stress (σ ys ), ultimate tensile stress (σ ut ), Young's modulus (E), and % elongation (% et) extracted from the stress-strain curves along with error bars are presented in Figure 4b-e. The positive strain rate dependency was observed for tensile yield stress for the temperatures considered in the study, as shown in Figure 4b. The highest yield stress variation of 2% between 0.01 s −1 to 0.1 s −1 and 0.1 s −1 to 1 s −1 was observed at −20 • C. However, the lowest yield stress variation between successive strain rates, around 0.5%, was noticed at 24 • C. It was observed that the yield stress decreased from −20 • C to room temperature and further increased slightly at 200 • C, indicating the V-shaped behavior for temperature variation.
Similarly, ultimate tensile stress exhibited the positive strain rate dependency at various temperatures, as shown in Figure 4c. However, strain rate has minimal effect on ultimate tensile stress as the difference observed between successive strain rates for all temperatures is less than 1%. The ultimate tensile stress is inversely proportional to the temperature for all the strain rates and is in line with the observations of Hafley et al. [5] and Chemin et al. [6] Figure 4d, shows the variation of Young's modulus at various strain rates and temperatures. Young's modulus showed negative strain rate sensitivity at room and higher temperatures. However, the strain rate effect on Young's modulus was negligible (around 1%) at −20 • C. The maximum Young's modulus difference of about 10% was observed at 200 • C between strain rates 0.01 and 1 s −1 . Furthermore, Young's modulus difference was around 5% at room temperature for successive strain rate variations. This reveals that the strain rate sensitivity towards Young's modulus was in the decreasing order of temperatures 1%) at −20 °C. The maximum Young's modulus difference of about 10% was observed at 200 °C between strain rates 0.01 and 1 s −1 . Furthermore, Young's modulus difference was around 5% at room temperature for successive strain rate variations. This reveals that the strain rate sensitivity towards Young's modulus was in the decreasing order of tempera-   Overall, a reduction between 6% and 10% is noticed in Young's modulus for the temperatures studied. The exact thickness of the plate with room temperature and −54 • C has been studied by Chemin et al. [6], revealing the same trend with a 2.5% reduction in Young's modulus. With a 100 mm (4-inch) plate, Hafley et al. [5] noticed a 9-11% reduction in Young's modulus when studied at different locations for room and −196 • C temperature.
Strong interatomic bonding between the atoms at room temperature may be the probable reason for the highest value of Young's modulus. Farraro Figure 4e shows the % elongation of AA2050-T84 alloy at different strain rates and temperatures. Negative strain rate dependency on % elongation as similar to Young's modulus was observed for various temperatures. The maximum % elongation was noticed at room temperature, indicating higher ductility than other temperatures.

Fracture Toughness Test Analysis
The fracture toughness tests were conducted as per ASTM E399-20a at different temperatures. ASTM E399-20a essentially elucidates the procedure of obtaining the single value, Plane Strain Fracture Toughness (K IC ), for metallic materials under quasi-static strain rates. The C(T) specimen was fatigue pre-cracked to emulate the natural crack characteristics. The effect of loading and material properties (mainly yield stress) strongly influences fatigue crack growth [35]. The pre-cracking load details are shown in Table 2. The load ratio (σ min /σ max ) was maintained at 0.1 to attain the a/W range in between 0.45 and 0.55. The pre-cracked C(T) specimen was tested under Mode-I (opening mode) loading through tensile load application at the holes. A minimum of 3 successful fracture toughness tests was conducted at each temperature at the strain rate 0.01 s −1 . The K IC (average of 3 test samples) obtained from experiments for −20 • C and 24 • C are 904.28 and 1059.36 MPa mm 1/2 , respectively. The error bar for the K IC is depicted in Figure 5.
been studied by Chemin et al. [6], revealing the same trend with a 2.5% reduction in Young's modulus. With a 100 mm (4-inch) plate, Hafley et al. [5] noticed a 9-11% reduction in Young's modulus when studied at different locations for room and −196 °C temperature.
Strong interatomic bonding between the atoms at room temperature may be the probable reason for the highest value of Young's modulus. Farraro and McLellan [34] have reported that the lower values of Young's modulus at elevated temperature indicate weakened interatomic bonding between the atoms. Figure 4e shows the % elongation of AA2050-T84 alloy at different strain rates and temperatures. Negative strain rate dependency on % elongation as similar to Young's modulus was observed for various temperatures. The maximum % elongation was noticed at room temperature, indicating higher ductility than other temperatures.

Fracture Toughness Test Analysis
The fracture toughness tests were conducted as per ASTM E399-20a at different temperatures. ASTM E399-20a essentially elucidates the procedure of obtaining the single value, Plane Strain Fracture Toughness (KIC), for metallic materials under quasi-static strain rates. The C(T) specimen was fatigue pre-cracked to emulate the natural crack characteristics. The effect of loading and material properties (mainly yield stress) strongly influences fatigue crack growth [35]. The pre-cracking load details are shown in Table 2. The load ratio (σmin / σmax) was maintained at 0.1 to attain the a/W range in between 0.45 and 0.55. The pre-cracked C(T) specimen was tested under Mode-I (opening mode) loading through tensile load application at the holes. A minimum of 3 successful fracture toughness tests was conducted at each temperature at the strain rate 0.01 s −1 . The KIC (average of 3 test samples) obtained from experiments for −20 °C and 24 °C are 904.28 and 1059.36 MPa mm 1/2 , respectively. The error bar for the KIC is depicted in Figure 5. At 200 • C, all the 3 test results were invalid as the ample crack deviation was observed from the crack plane. However, the K IC has reduced by about 15% from room to subzero temperature. Similarly, in the work of Chemin et al. [6], a reduction of the order of magnitude 16% in K IC was noticed in the rolling direction of the AA2050-T84 alloy plate from room to cryogenic (−56 • C) temperature. The decrease of K IC at sub-zero temperatures of AA2050-T84 alloy can be attributed to surface hardening inside the grain and validated by the grain microstructure of the alloy [6,36]. In summary, the positive temperature dependency was witnessed for K IC of AA2050-T84 alloy at strain rate 0.01 s −1 . The economic limitations on conducting further fracture toughness tests at other strain rates impelled us to adopt the numerical analysis.

Linear Elastic Fracture Analysis
ASTM E399-20a, to predict the K IC of metallic materials, recommended the single toughness value for lower strain rate variations. However, the variation of tensile properties of AA2050-T84 alloy at different lower strain rates and temperatures was substantial. The elastic fracture analysis was carried out at varied strain rates and temperatures using the Abaqus software. The current numerical procedure was adopted from Kudari et al. [22] and Kavale et al. [37] The K I values extracted through-thickness direction of the crack at 24 • C conditions, and experimental K IC are shown in Figure 6. The experimental K IC value was emulated through numerical fracture analysis with less than 1% error, as observed in Figure 6. from room to cryogenic (−56 °C) temperature. The decrease of KIC at sub-zero temperatures of AA2050-T84 alloy can be attributed to surface hardening inside the grain and validated by the grain microstructure of the alloy [6,36]. In summary, the positive temperature dependency was witnessed for KIC of AA2050-T84 alloy at strain rate 0.01 s −1 . The economic limitations on conducting further fracture toughness tests at other strain rates impelled us to adopt the numerical analysis.

Linear Elastic Fracture Analysis
ASTM E399-20a, to predict the KIC of metallic materials, recommended the single toughness value for lower strain rate variations. However, the variation of tensile properties of AA2050-T84 alloy at different lower strain rates and temperatures was substantial. The elastic fracture analysis was carried out at varied strain rates and temperatures using the Abaqus software. The current numerical procedure was adopted from Kudari et al. [22] and Kavale et al. [37] The KI values extracted through-thickness direction of the crack at 24 °C conditions, and experimental KIC are shown in Figure 6. The experimental KIC value was emulated through numerical fracture analysis with less than 1% error, as observed in Figure 6.
Similarly, at −20 °C, the validation of the numerical procedure was executed with less than 1% error. For all the numerical analysis, the center of the crack front was associated with the largest value of the crack characterizing parameter. Thus, the KI values at the center of the specimen are used for analysis in further discussions.

Effect of Strain Rate
In linear elastic fracture analysis, the experimental load associated with KIC of the alloy is the applied load at respective temperatures. However, the KIC at 200 °C was unavailable, and hence for the numerical analysis, the assumed load applied up to KI = 1200 MPa mm 1/2 . The applied stress (σapplied) was determined using the relationship mentioned in Equation (2) [27]. The extracted values of KI at the crack front center for various strain rates and temperatures are plotted against the stress ratio (σapplied/σys) as shown in Figure  7. Positive strain rate dependency of the KI was observed for all temperatures considered Similarly, at −20 • C, the validation of the numerical procedure was executed with less than 1% error. For all the numerical analysis, the center of the crack front was associated with the largest value of the crack characterizing parameter. Thus, the K I values at the center of the specimen are used for analysis in further discussions.

Effect of Strain Rate
In linear elastic fracture analysis, the experimental load associated with K IC of the alloy is the applied load at respective temperatures. However, the K IC at 200 • C was unavailable, and hence for the numerical analysis, the assumed load applied up to K I = 1200 MPa mm 1/2 . The applied stress (σ applied ) was determined using the relationship mentioned in Equation (2) [27]. The extracted values of K I at the crack front center for various strain rates and temperatures are plotted against the stress ratio (σ applied /σ ys ) as shown in Figure 7. Positive strain rate dependency of the K I was observed for all temperatures considered in this study. At room temperature, a steady increase of 0.6% in K I was witnessed with the rise in strain rate. However, for strain rate 1 s −1 , the maximum of 1.88% increase in K I was noticed at −20 • C. The strain rate sensitivity on K I was found to be maximum at −20 • C and minimum at 24 • C, as the same trend was noticed for tensile yield stress values. The results of the K I are in line with the yield stress variations of the alloy for all strain rates at different temperatures. The nominal variations of K I (within the stress ratio of K IC ) indicate the negligible dependency of fracture characterizing parameters on strain rates for AA2050-T84 alloy. Moreover, ASTM E399-20a recommendation to use the single value of K IC for quasi-static strain rates seems to be justifying as the difference in numerical K I values was minimal. 2) in this study. At room temperature, a steady increase of 0.6% in KI was witnessed with the rise in strain rate. However, for strain rate 1 s −1 , the maximum of 1.88% increase in KI was noticed at −20 °C. The strain rate sensitivity on KI was found to be maximum at −20 °C and minimum at 24 °C, as the same trend was noticed for tensile yield stress values. The results of the KI are in line with the yield stress variations of the alloy for all strain rates at different temperatures. The nominal variations of KI (within the stress ratio of KIC) indicate the negligible dependency of fracture characterizing parameters on strain rates for AA2050-T84 alloy. Moreover, ASTM E399-20a recommendation to use the single value of KIC for quasistatic strain rates seems to be justifying as the difference in numerical KI values was minimal. Further, the effect of strain rate on crack tip/front constraints has been evaluated through T11 and T33. The values of T11 and T33 are found to vary along the thickness similar to KI variation and maximum being at the center of the specimen. One can infer that the crack-front constraint is high at the center than at the surface; the material may fail at the center than on surface or shows instability at the center of the specimen. As the constraint parameters do not have a unique value for the specimen thickness, maximum values at the center of the specimen are considered for further analysis. T11 and T33 variations for Further, the effect of strain rate on crack tip/front constraints has been evaluated through T 11 and T 33 . The values of T 11 and T 33 are found to vary along the thickness similar to K I variation and maximum being at the center of the specimen. One can infer that the crack-front constraint is high at the center than at the surface; the material may fail at the center than on surface or shows instability at the center of the specimen. As the constraint parameters do not have a unique value for the specimen thickness, maximum values at the center of the specimen are considered for further analysis. T 11 and T 33 variations for different strain rates within the purview of K IC (or stress ratio) of the alloy at respective temperatures are plotted in Figure 8. The nature of variation was identical at all strain rates for both constraint parameters. However, the increase in stress ratio resulted in positive T 11 and negative T 33 values at all strain rates and temperatures. It is clear from Figure 8, that the applied stress was directly proportional to T 11 and inversely proportional to T 33 . The negative strain along the thickness resulted in the negative T 33 [20]. This is in close agreement with the findings of Kudari et al. [22] for IF steel C(T) specimen. agreement with the findings of Kudari et al. [22] for IF steel C(T) specimen.
At 24 °C and 200 °C, both constraint parameters were unaffected (very marginal difference) by the strain rate variation, as observed in Figure 8b,c. However, T33 variations between the strain rates at −20 °C were relatively substantial. At −20 °C, between the strain rates, a difference of 2.4% was found for T33. T33 variation depended on Poisson's ratio and Young's modulus (material property) of the alloy at different strain rates. Eventually, the crack driving and constraint parameters were less sensitive to strain rate variations. Strain rate effect on T11 variation is negligible as in-plane constraint depends on specimen type, geometry, and loading type only. Furthermore, the variation of hydrostatic stress along the uncracked ligament is studied at different strain rates. It is observed that no variations are found at different strain rates. The negligible variation of T11 can also be attributed to the uniform state of stress at the crack front and minimal variation of yield stress (or stress ratio as depicted in the graph) between the strain rates. However, the T33 variation is quite measurable at different strain rates for −20 °C, as shown in Figure 8a, owing to the variations in material property (both Young's modulus and yield stress). At 24 • C and 200 • C, both constraint parameters were unaffected (very marginal difference) by the strain rate variation, as observed in Figure 8b,c. However, T 33 variations between the strain rates at −20 • C were relatively substantial. At −20 • C, between the strain rates, a difference of 2.4% was found for T 33 . T 33 variation depended on Poisson's ratio and Young's modulus (material property) of the alloy at different strain rates. Eventually, the crack driving and constraint parameters were less sensitive to strain rate variations.
Strain rate effect on T 11 variation is negligible as in-plane constraint depends on specimen type, geometry, and loading type only. Furthermore, the variation of hydrostatic stress along the uncracked ligament is studied at different strain rates. It is observed that no variations are found at different strain rates. The negligible variation of T 11 can also be attributed to the uniform state of stress at the crack front and minimal variation of yield stress (or stress ratio as depicted in the graph) between the strain rates. However, the T 33 variation is quite measurable at different strain rates for −20 • C, as shown in Figure 8a, owing to the variations in material property (both Young's modulus and yield stress). Positive T 11 results in a lower plastic zone at the crack tip and influences the specimen's unstable crack growth. Similarly, negative T 33 results in loss of constraint at the crack tip.
Since the crack front plasticity is restricted in LEFM regime, the state of stress may be unaltered due to strain rate variations at identical temperatures. The current serrated stress-strain curves may affect the plasticity ahead of the crack front and can be accounted in Elastic-Plastic Fracture Mechanics (EPFM) regime.

Effect of Temperature
The variation of K I at different temperatures for quasi-static strain rates is plotted in Figure 9. The K I variation is linearly increased with an increase in stress ratio as expected, and the nature of variation was the same for all temperatures considered. At the peak stress ratio, the difference between K I at 200 • C and −20 • C is 5.1%, 5.16%, and 7.31% at strain rates 0.01, 0.1, and 1 s −1 , respectively. However, the variation of K I was minimum (around 4%) for the temperatures 24 • C and 200 • C at all strain rates. Notably, the temperature effect was highest at strain rate 1 s −1 and in the decreasing order of 1: 0.1: 0.01 s −1 . The substantial variation of K I at sub-zero temperatures indicates that for identical load conditions, the AA2050-T84 alloy is more prone to fracture failure than the other two temperatures as it possesses lower K IC.
Positive T11 results in a lower plastic zone at the crack tip and influences the specimen's unstable crack growth. Similarly, negative T33 results in loss of constraint at the crack tip.
Since the crack front plasticity is restricted in LEFM regime, the state of stress may be unaltered due to strain rate variations at identical temperatures. The current serrated stress-strain curves may affect the plasticity ahead of the crack front and can be accounted in Elastic-Plastic Fracture Mechanics (EPFM) regime.

Effect of Temperature
The variation of KI at different temperatures for quasi-static strain rates is plotted in Figure 9. The KI variation is linearly increased with an increase in stress ratio as expected, and the nature of variation was the same for all temperatures considered. At the peak stress ratio, the difference between KI at 200 °C and −20 °C is 5.1%, 5.16%, and 7.31% at strain rates 0.01, 0.1, and 1 s −1 , respectively. However, the variation of KI was minimum (around 4%) for the temperatures 24 °C and 200 °C at all strain rates. Notably, the temperature effect was highest at strain rate 1 s −1 and in the decreasing order of 1: 0.1: 0.01 s −1 . The substantial variation of KI at sub-zero temperatures indicates that for identical load conditions, the AA2050-T84 alloy is more prone to fracture failure than the other two temperatures as it possesses lower KIC. Similarly, Figure 10 shows the variation of T 11 and T 33 at different temperatures for quasi-static strain rates. The variation of T 11 and T 33 were almost identical at 24 • C and 200 • C at quasi-static strain rates. At 200 • C, the T 11 was less subtle and owed lower in-plane constraints than the −20 • C, and 24 • C. Chemin et al. [6] have related dislocations gathered along the grain boundaries, led to stress concentrations under loading and promoted the lower fracture toughness of the AA2050-T84 alloy at sub-zero (−56 • C) temperature. Similarly, in the current analysis, the sensitivity of fracture toughness and in-plane constraint against the stress ratio is highest at −20 • C. The sensitivity may be associated to crack front stress concentrations at grain boundaries at −20 • C and can be accounted through constraint parameters as shown in the current numerical analysis. However, the T 11 and T 33 variations seem identical for strain rates 0.01 and 1 s −1 through Figure 10a,c at −20 • C. Eventually, T 11 and T 33 in combination with K I is maximum at 1 s −1 compared to 0.01 s −1 . Thus, the highest constraint associated with numerically obtained K I of the AA2050-T84 alloy at −20 • C is 1 s −1 . This behavior also resulted in the lower K IC at −20 • C than 24 • C. lower fracture toughness of the AA2050-T84 alloy at sub-zero (−56 °C) temperature. Similarly, in the current analysis, the sensitivity of fracture toughness and in-plane constraint against the stress ratio is highest at −20 °C. The sensitivity may be associated to crack front stress concentrations at grain boundaries at −20 °C and can be accounted through constraint parameters as shown in the current numerical analysis. However, the T11 and T33 variations seem identical for strain rates 0.01 and 1 s −1 through Figure 10a,c at −20 °C. Eventually, T11 and T33 in combination with KI is maximum at 1 s −1 compared to 0.01 s −1 . Thus, the highest constraint associated with numerically obtained KI of the AA2050-T84 alloy at −20 °C is 1 s −1 . This behavior also resulted in the lower KIC at −20 °C than 24 °C.
In summary, the major constraint loss was observed for temperature variation compared to quasi-static strain rate variations. Moreover, at −20 °C, AA2050-T84 alloy possesses lower KIC with the highest in-plane crack tip/front constraint compared to the other two temperatures. This behavior of the alloy makes it vulnerable to fracture failure in cryogenic (sub-zero) applications at a strain rate 1 s −1 .   In summary, the major constraint loss was observed for temperature variation compared to quasi-static strain rate variations. Moreover, at −20 • C, AA2050-T84 alloy possesses lower K IC with the highest in-plane crack tip/front constraint compared to the other two temperatures. This behavior of the alloy makes it vulnerable to fracture failure in cryogenic (sub-zero) applications at a strain rate 1 s −1 .

Conclusions
In the present study, the tensile and fracture behavior of the 50 mm thick (2-inch) AA2050-T84 plate was considered at various temperatures for quasi-static strain rates. Tensile tests revealed the sensitivity of mechanical properties towards the strain rates and temperatures. Positive strain rate dependency was observed for temperatures considered on yield stress and ultimate tensile stress of the alloy. A maximum of 2% increase in yield stress was noticed between strain rates at −20 • C. The lowest strain rate sensitivity of around 0.5% was witnessed at room temperature. Notably, the ultimate stress variation between the strain rates for temperatures was less than 1%. However, Young's modulus and % elongation were negative strain rate dependent. The maximum decrease of Young's modulus up to 10% was noticed at 200 • C. The minimum Young's modulus variation was witnessed at −20 • C between the strain rates.
Temperature sensitivity towards tensile behavior of the AA2050-T84 alloy was noticed. The maximum yield stress variation of 10-11% was witnessed between room temperature and −20 • C. Notably, the yield stress increase was only up to 3% between room temperature and 200 • C. Similarly, for ultimate stress, the variation was up to 7.5% between room temperature and −20 • C. However, the reduction of Young's modulus up to 18% was noticed between room temperature and 200 • C. This implies that yield and ultimate stress are quite substantial at −20 • C compared to other temperatures, making the AA2050-T84 alloy vulnerable at sub-zero temperatures. Moreover, an increase in strain rate prompts the decrease in % elongation, implying the brittle behavior of the alloy at higher strain rates.
The crack driving and constraint parameters are less sensitive to strain rate variations. However, at −20 • C, crack characterizing and constraint parameters to strain rate variations were moderately considerable. The temperature effect is highest at strain rate 1 s −1 and in the decreasing order of 1:0.1:0.01 s −1 .
Overall, the AA2050-T84 alloy tensile and fracture performance obtained through experimental and numerical analyses exhibited the dependency on strain rates and temperatures. Hence, these mechanical properties of the alloy strongly influence the damage tolerance design of spars and wings of the aircraft. The authors believe that the current results concerning strain rates and temperatures will help in understanding the performance-related issues of AA2050-T84 alloy reported in aircraft applications. Data Availability Statement: This study didn't report any data.